"The President's sequester is the wrong way to reduce the deficit, but it is here to stay until Washington Democrats get serious about cutting spending," Boehner writes. "The government simply cannot keep delaying the inevitable and spending money it doesn't have."

Boehner is arguing that the sequester will be incredibly damaging — it "threatens U.S. national security, thousands of jobs and more." But at the same time, Republicans are prepared to let the sequester kick in if Democrats don't agree to an equal amount of cuts in entitlement spending. In essence, Boehner is prepared to support a policy that he says threatens national security and jobs.

Could the GOP message on the sequester be any more self-defeating? Boehner could argue that the sequester cuts are necessary as a first — and somewhat modest — step toward controlling the deficits that threaten the economy. Instead, he describes them as a threat to national security and jobs that he nevertheless supports. It’s not an argument that is likely to persuade millions of Americans.

"The President believes it is essential that we avoid these cuts," Carney said after reading a passage from York's piece. "It is bad policy. The Speaker himself says it is bad policy. We — the Congress, rather, must act to make sure it doesn’t happen."

On the other end of the spectrum, conservative radio host Rush Limbaughalso cited York's piece and wondered "what Speaker Boehner is thinking."

"But the question is, why would Republicans support something that does what Boehner says it's gonna do?" Limbaugh said. "... I do not have an explanation. I don't think that there is a reasonable explanation for that. I don't understand it. Don't have an answer for you. It's too simple to chalk this up to incompetence. It may be that, but that's too simple. I don't have an answer. I can't explain it to you. All I know is that it doesn't make any sense."

Mixed messaging can only add to the GOP's woes, because on its surface, letting the sequester go into effect doesn't look like a winning game. That's because although his approval ratings have fallen after a post-election honeymoon, Obama is still viewed far more favorably than Congressional Republicans.